Theory of Zeeman Effect for Rare-Earth Ions in Crystal Field with C3h Symmetry. III

An analysis is made of several strikingly regular Zeeman patterns which have been observed in the optical absorption spectrum of erbium ions in ethylsulfate crystals. In the experiments the magnetic field was applied in the basal plane, and the light was shone in perpendicular to both the $c$ axis and the magnetic field. It was polarized either in the direction of the $c$ axis or the magnetic field. The spectra were observed as a function of orientation of the crystal about the $c$ axis. In most of the Zeeman patterns there is a complicated dependence of the frequencies and intensities of the lines on the crystal orientation. In the three special cases analyzed here the frequencies are independent of orientation and the intensities are constant or vary in a sixfold way. It is shown that the energies and intensities of these patterns can be well understood by restricting the Zeeman contribution to the rare‐earth‐ion Hamiltonian to interaction within a small set of crystal‐field states in the appropriate multiplet. This is a reasonable approximation to make for the transitions studied because the particular energy levels involved remain isolated from the others throughout the range of magnetic‐field strengths used $\text{(H\hspace{0.17em}<\hspace{0.17em}30 kG).}$ Comparison of the theoretical and experimental results determines some of the parameters in the calculation and provides new information about the odd‐parity part of the $C_{\text{3h}}$ environment of Er³⁺ in the ethylsulfate lattice. In particular, the results suggest that the major contribution to the departure from effective $D_{\text{3h}}$ symmetry at the rare‐earth‐ion site is provided by the ${\mathfrak{Y}}_{\text{3±3}}$ terms in the crystal‐field expansion rather than by ${\mathfrak{Y}}_{\text{5±3}}$ and ${\mathfrak{Y}}_{\text{7±3}}$ terms.